# Tagged Questions

Questions about the branch of abstract algebra that deals with groups.

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### Positivity of the alternating sum of indices for boolean interval of finite groups

Let $G$ be a finite group and $H$ a subgroup such that the interval $[H,G]$ is a boolean lattice. Let $L_1, \dots , L_n$ be the maximal subgroups of $G$ containing $H$. Let the alternative sum ...
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### the braid groups on the sphere

The braid group $B_n(S^2)$ on the sphere possesses a finite element of order which generates a cyclic group $M$ in $B_n(S^2)$. My question is this: What is the index of $H$ in $B_n (S^2)$? Same ...
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### Dicks–Dunwoody almost stability theorem

In the book 'Groups acting on graphs' (1989), Dicks and Dunwoody prove the following theorem (paraphrased): Let $G$ be a group acting on a set $E$, let $E'$ be a subset of $E$ and let $V$ be the set ...
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### Can the reversed lattice of a subgroups interval be represented?

Let $G$ be a finite group and $H$ a subgroup. The interval $[H,G]$ is the lattice of overgroups of $H$. It is an open problem to know if every finite lattice can be represented by such an interval (...
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### Infinite finitely generated groups whose Frattini factors are Klein 4-group

Is there an infinite finitely generated group whose Frattini factor is isomorphic to Klein 4-group?
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### Maximal set of non commuting elements in a conjugacy class of $S_8$

Can someone calculate by computer or prove the subset of maximal order of pairwise non commuting elements in the set of conjugacy class containing $(123)(45)$ in $S_8$? I mean a subset of conjugacy ...